Bill Clinton and Al Leiter emerged from the players’ lounge inside the Met clubhouse yesterday shoulder to shoulder. The former president and the Met left-hander seemed like good buddies, even though their politics point in opposite directions.

Leiter, who’s talked about going into politics after his playing career, is a registered Republican who campaigned for Mayor Bloomberg.

“You call me some time,” Clinton told Leiter, slapping him on the back for good measure.

Clinton made an unannounced visit to Shea Stadium, glad-handing players and fans and speaking about, among other things, Leiter’s future in politics.

“I can’t do anything for his pitching career,” Clinton joked.

But the 42nd president said did call Leiter “competitive and inquisitive,” adding, “I think both of those things are important. Who knows? Maybe if we had a month to work on each other, one of us would switch.”

Leiter wasn’t always so friendly toward Clinton.

In 1997, after Leiter’s Marlins won the World Series, the pitcher didn’t accompany the team to Clinton’s White House.

As Leiter recalled in a 2001 interview with The Post, “I didn’t care to see him. I didn’t really have a whole lot of respect for him. . . . It was right during the whole Monica Lewinsky thing, and I think the guy made a mockery of the whole White House.”

Last night, Leiter said he had a blast talking politics with the former president – and was the consummate diplomat when asked about his absence at that 1997 ceremony.

He said because the Marlins were dismantled in the offseason, he was in spring training with the Mets.

“I had the choice. I think it was more of an inconvenience,” Leiter said. “You absolutely respect him holding the most powerful office in the world.”

Asked if he would’ve attended the ceremony had there been an incumbent Republican, Leiter paused and responded, “I might’ve, but probably not. It was more of an inconvenience than anything.”